Data structures' project
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The document discusses Huffman coding, a method for data compression that assigns variable-length codes to input characters based on their frequency of occurrence. It involves building a binary tree from the character frequencies and assigning shorter codes to more common characters. This allows for more efficient representation of data compared to fixed-length codes like ASCII. Applications include compression in file formats like MP3 and JPEG.
Data structures' project
- 2. COMSATS Institute of Information & Technology, Islamabad Subject : Data Structures A presentation by Ayesha Arif FA10-BSB-014 & Ghazanfar Ali Baig FA10-BSB-024 Instructor Name: Ms. Nusrat Shaheen
- 4. Background • When we encode characters in computers, we assign each an 8-bit code based on an ASCII chart. • But in most files, some characters appear more often than others. • So wouldn't it make more sense to assign shorter codes for characters that appear more often and longer codes for characters that appear less often?
- 5. Data Compressions • Lossless compressions: Less space is used, or energy to transmit it. –No information is lost –we can reconstruct the original text –Often: be able to quickly reconstruct original text • Lossy compressions.
- 6. Data Compressions • Text representation: • ASCII: 1 byte per character (fixed length code) – “M A R C” 1st Byte 2nd Byte 3rd Byte 4th byte 77 97 114 99 01001101 01100001 01110010 01100011
- 7. • In the English language, the letter „e‟ is, „quite common x‟ is less common–Why should all characters be represented using the same number of bits?
- 8. Huffman • 1951, David Huffman found the “most efficient method of representing numbers, letters, and other symbols using binary code” • Now standard method used for data compression
- 9. The Concept • Huffman coding has the following properties: • Codes for more probable characters are shorter than ones for less probable characters. • Each code can be uniquely decoded .
- 10. The Concept • To read the codes from a Huffman tree, start from the root and add a '0' every time you go left to a child, and add a '1' every time you go right. So in this example, the code for the character 'b' is 01 and the code for 'd' is 110. • As you can see, 'a' has a shorter code than 'd'. Notice that since all the characters are at the leafs of the tree (the ends), there is never a chance that one code will be the prefix of another one (eg. 'a' is 00 and 'b' is 011 • ). • Hence, this unique prefix property assures that each code can be uniquely decoded.
- 11. Huffman Codes • How to construct Huffman codes? • Build a binary tree!
- 12. Binary Tree • A binary tree is a tree where each internal node has at most 2 children.
- 13. Internal The “Root Node” A Vertex The “Left Node” B C The “Right Node” D E F G Sibling Nodes Leaf Binary Tree Vertex
- 14. Algorithm 1.Take the characters and their frequencies, and this list by increasing frequency. 2 .All the characters are vertices of the tree. 3.Take the first 2 vertices from the list and make them children of a vertex having the sum of their frequencies. 4.Insert the new vertex into the sorted list of vertices waiting to be put into the tree. 5.If there are at least 2 vertices in the list, go to step 3. 6.Read the Huffman code from the tree.
- 15. Huffman’s Code 1.Take the characters and their frequencies, and sort this list by increasing frequency A: 3, O: 5, T: 7, E:10
- 16. Huffman’s Code 2. All the characters are the vertices of the tree: A:3 O:5 T:7 E:10
- 17. Huffman’s Code 3 .Take the first two vertices from the list and make them children of a vertex having the sum of their frequencies *:8 A:3 O:5
- 18. Huffman’s Code 4 .Insert the new vertex into the sorted list of vertices waiting to be put into tree T:7 E:10 • List of remaining vertices • New list, with the new vertex T:7 8 E:10 inserted
- 19. Huffman’s Code *: 15 5. Take the first 2 vertices from the list and make them T:7 *: 8 Children of the vertex having the sum of their frequencies. A:3 O:5
- 20. Huffman’s Code 6. Insert the new vertex into the sorted list of vertices waiting to be put into tree. • List of remaining vertices E:10 • New list, with the E:10 * : 15 new vertex inserted
- 21. *:25 New vertex with frequency 10 +15 = 25 7. Take the E:10 *:15 first two Vertices from the list and make them children of T:7 *:8 the vertex having the sum of their frequencies. A:3 O:5
- 22. Huffman’ *:25 s Code 0 1 E:10 *:15 • Left branch = 0 1 0 • Right branch = 1 • Huffman Code T:7 *:8 E:0 T:10 1 0 A:110 O: 111 A:3 O:5
- 23. Advantage of Huffman Codes • Reduce size of data by 20%-90% in general • If no characters occur more frequently than others, then no advantage over ASCII. • Encoding: –Given the characters and their frequencies, perform the algorithm and generate a code. Write the characters using the code. • Decoding: Given the Huffman tree, figure out what each character is (possible because of prefix property).
- 24. Applications • Both the .mp3 and .jpg file formats use Huffman coding at one stage of the compression. • Alternative method that achieves higher compression but is slower is patented by IBM, making Huffman Codes attractively.
- 25. Program
- 26. References •http://www.siggraph.org/education/materials/Hy perGraph/video/mpeg/mpegfaq/huffman_tutori al.html • http://www.huffmancoding.com/david/algorith m.html • http://www.cs.sfu.ca/CourseCentral/365/li/squ eeze/Huffman.htm